Question

what equation does this set of algebra tiles represent?
five green tiles labeled x = five orange tiles labeled 1 (arranged as two rows of two and one row of one)
combine like terms on each side of the equation. for example, write 1 + 1.

Explanation:

Step1: Analyze left - hand side

The left - hand side has 5 tiles each labeled \(x\). So the left - hand side can be represented as \(5x\) (since we are adding \(x\) five times, and by the definition of multiplication, \(x + x+ x + x + x=5x\)).

Step2: Analyze right - hand side

The right - hand side has 5 tiles each labeled 1. So the right - hand side can be represented as \(1 + 1+1 + 1+1\). Combining these like terms (since all the terms are constants of 1), we get \(5\times1 = 5\).

Step3: Form the equation

Putting the left - hand side and the right - hand side together, the equation is \(5x=5\). And when we combine like terms on each side, the left - hand side is \(5x\) and the right - hand side is \(1 + 1+1 + 1+1 = 5\), so the simplified form after combining like terms is \(5x = 5\).

Answer:

The equation represented by the algebra tiles is \(5x=5\) (after combining like terms, the left - hand side is \(5x\) and the right - hand side is \(1 + 1+1 + 1+1=5\), so the equation is \(5x = 5\)).